find the equation of the plane containing 2 parallel lines x-1/2 = y+1 / -1 = z/3 and x/4 - Maths - Three Dimensional Geometry

Question

find the equation of the plane containing 2 parallel lines x-1/2 =
y+1 / -1 = z/3 and x/4 = y-2/-2 = z+1/6 also find the plane thus
obtained contains the line x-2/3 = y-1/1 = z-2 /5 or not

Lovina Kansal · Accepted Answer

Dear student
We know that the equation of the plane containing two given parallel lines
x-x1a=y-y1b=z-z1c and x-x2a=y-y2b=z-z2c  isx-x1y-y1z-z1x2-x1y2-y1z2-z1abc=0Here, x1=1,y1=-1 ,z1=0,x2=0,y2=2,z2=-1l1=2,m1=-1,n1=3,l2=4,m2=-2,n2=6Now,x-1y+1z-12-(-1)-12-13=0⇒x-1y+1z-12-12-13=0⇒5x-1-1y+1-3z=0⇒5x-5-y-1-3z=0⇒5x-y-3z-6=0
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find the equation of the plane containing 2 parallel lines x-1/2 = y+1 / -1 = z/3 and x/4 = y-2/-2 = z+1/6 . also find the plane thus obtained contains the line x-2/3 = y-1/1 = z-2 /5 or not